OPTIMIZATION AND SENSITIVITY ANALYSIS FOR MULTIRESPONSE PARAMETER-ESTIMATION IN SYSTEMS OF ORDINARY DIFFERENTIAL-EQUATIONS

Methodology for the simultaneous solution of ordinary differential equ ations (ODEs) and associated parametric sensitivity equations using th e Decoupled Direct Method (DDM) is presented with respect to its appli cability to multiresponse parameter estimation for systems described b y nonlinear ordinary differential equations. The DDM is extended to pr ovide second order sensitivity coefficients and incorporated in multir esponse parameter estimation algorithms utilizing a modified Newton sc heme as well as a hybrid Newton/Gauss-Newton optimization algorithm. S ignificant improvements in performance are observed with use of both t he second order sensitivities and hybrid optimization method. In this work, our extension of the DDM to evaluate second order sensitivities and development of new hybrid estimation techniques provide ways to mi nimize the well-known drawbacks normally associated with second-order optimization methods and expand the possibility of realizing their ben efits, particularly for multiresponse parameter estimation in systems of ODEs.